1. **Problem Statement:** We are given a parallelogram with angles labeled as $44^\circ$, $52^\circ$, $y^\circ$, $x^\circ$, and $97^\circ$. We need to find the values of $x$ and $y$. 2. **Properties of a Parallelogram:** Opposite angles in a parallelogram are equal, and adjacent angles are supplementary (sum to $180^\circ$). 3. **Using the Supplementary Angle Rule:** Since $44^\circ$ and $x^\circ$ are adjacent angles, they satisfy: $$44 + x = 180$$ 4. **Solving for $x$:** $$x = 180 - 44 = 136$$ 5. **Using the Opposite Angle Rule:** The angle opposite to $y^\circ$ is $52^\circ$, so: $$y = 52$$ 6. **Verification:** Adjacent to $y$ is $97^\circ$, check if they sum to $180^\circ$: $$y + 97 = 52 + 97 = 149 \neq 180$$ This suggests $97^\circ$ is not adjacent to $y$, so no conflict. **Final answers:** $$x = 136^\circ$$ $$y = 52^\circ$$